A building cost $800,000 new and has accrued depreciation of $200,000. The land value is $150,000. Using the extraction method, if the property sold for $720,000, what is the indicated land value?
Correct Answer
A) $120,000
Extraction method: Land Value = Sale Price - Depreciated Building Value. Depreciated building value = $800,000 - $200,000 = $600,000. Land value = $720,000 - $600,000 = $120,000.
Why This Is the Correct Answer
Option A ($120,000) correctly applies the extraction method formula. First, we calculate the depreciated building value: $800,000 (new cost) - $200,000 (accrued depreciation) = $600,000. Then we extract the land value: $720,000 (sale price) - $600,000 (depreciated building value) = $120,000. This represents what the market is actually paying for the land component based on the actual sale transaction.
Why the Other Options Are Wrong
Option B: $150,000
Option B ($150,000) incorrectly uses the given land value from the problem statement rather than calculating the extracted land value from the sale. This figure represents an assumed or previously estimated land value, not the market-indicated value derived from the actual sale transaction.
Option C: $320,000
Option C ($320,000) appears to subtract only the accrued depreciation from the sale price ($720,000 - $200,000 = $520,000) or uses some other incorrect calculation. This fails to account for the full depreciated building value and does not follow the proper extraction method formula.
Option D: $570,000
Option D ($570,000) incorrectly subtracts the given land value from the sale price ($720,000 - $150,000 = $570,000), which reverses the extraction logic and would represent a building value rather than land value. This demonstrates a fundamental misunderstanding of the extraction method.
SALE minus BUILDING equals LAND
Remember 'SBL' - Sale price minus (depreciated) Building value equals Land value. Think of 'extracting' the land like removing a building from a property - you take away the building value from the total to get what's left (the land).
How to use: When you see extraction method questions, immediately write 'Sale - Building = Land' and identify: 1) Sale price, 2) Calculate depreciated building value (cost new minus depreciation), 3) Subtract to find land value.
Exam Tip
Always calculate the depreciated building value first (replacement cost new minus accrued depreciation) before applying the extraction formula, and don't be distracted by any given land values in the problem.
Common Mistakes to Avoid
- -Using the given land value instead of calculating the extracted value
- -Forgetting to subtract accrued depreciation from replacement cost new
- -Confusing the formula and subtracting sale price from building value
Concept Deep Dive
Analysis
The extraction method is a land valuation technique used when comparable land sales are not available, requiring the appraiser to 'extract' the land value from an improved property sale. This method assumes that the total property value equals the sum of land value plus the depreciated replacement cost of improvements. The extraction method is particularly useful in areas where vacant land sales are rare or when valuing unique properties. It relies on accurate cost estimates and depreciation calculations to isolate the land component from the total sale price.
Background Knowledge
The extraction method is one of several land valuation techniques used when direct land sales comparables are unavailable. It requires accurate knowledge of replacement cost new, proper depreciation estimation, and assumes the sale price represents market value.
Real-World Application
Appraisers use extraction method when valuing properties in areas with limited vacant land sales, such as fully developed urban areas or when appraising unique properties like gas stations or churches where land comparables are scarce.
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